Syntax

Aether source is statement-oriented. Newlines and ~ can terminate statements.

Literals And Variables

let x = 10~
let y = 3.14~
let ok = true~
let name = "aether"~
let values = [1.0, 2.0, 3.0]~

The parser accepts optional type-hint style declarations:

point C = [1.0, 2.0, 3.0]~

Current type hints are parsed as syntax. They are not a full static type system.

Expressions

Active expression operators:

• arithmetic: +, -, *, /, %;
• comparison: <, >, <=, >=, ==, !=;
• logical: &&, ||, !;
• ranges: 0..4 for for loops and 0:64 for slices.

Control Flow

if count == 0 {
  print("empty")~
} else {
  print("nonempty")~
}

while count < 3 {
  count = count + 1~
}

for i in 0..4 {
  total = total + i~
}

break and continue are active inside loops.

Seal Loop

seal until count >= 3 {
  count = count + 1~
}

A seal loop has three stopping rules, all capped at 1,000 passes.

Condition	Stops	Kind
until expr	before a pass, when expr is true	any boolean
until convergence(ε)	after pass \(i \ge 2\) with \(d(v_i, v_{i-1}) \le \varepsilon\)	scalar tolerance
until stable(expr)	before a pass, when expr equals its value one pass earlier	exact invariant

For convergence, \(v_i\) is the value of the body's last statement after pass \(i\), and \(d\) is the max norm: \(\lvert x - y \rvert\) on numbers, the maximum over elements on lists and records of equal shape (\(+\infty\) if the shape changes), and the difference of final_error on regression results. A body value with no distance, and a negative \(\varepsilon\), are refused by name.

let x = 1~
let n = 0~
🦭 until convergence(1e-6) {
  n = n + 1~
  x = (x + 2 / x) / 2~
  x~
}
print([n, x])~

Newton's iteration for \(\sqrt2\) prints [5, 1.414213562373095]. The fourth pass moves \(x\) by \(2.1\times10^{-6}\) and the fifth by \(1.6\times10^{-12}\). crates/aether-lang/tests/seal_convergence.rs pins this case.

stable is the topological form when the watched value is topological. For example, seal until stable(topology.betti(topology.ph(M), radius=r)) stops on a Betti vector, and seal until stable(euler(segs).faces) stops on a certified face count (see Integrated Mathematics). Equality is exact, so stability is a one-pass window.

Numeric literals are six-decimal fixed point. Exponents (1e-6, 2.5e3) scale them exactly. A literal the representation cannot hold, such as 1e-7, is a lexer error rather than a silent zero. Parentheses group: (x + 2 / x) / 2.

Functions

fn add(a, b) {
  return a + b~
}

let result = add(2, 3)~

Functions return explicit return values or the last value produced by the body.

Manifolds And Blocks

let data = [1.0, 2.0, 3.0, 4.0]~
manifold M = embed(data, tau=1)~
block B = M.cluster(0:2)~

The active interpreter uses a fixed 3D embedding workspace. tau is used. dim can be parsed but is not the runtime dimension selector in the current interpreter path.